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Theorem caovdig 6253
 Description: Convert an operation distributive law to class notation. (Contributed by NM, 25-Aug-1995.) (Revised by Mario Carneiro, 26-Jul-2014.)
Hypothesis
Ref Expression
caovdig.1
Assertion
Ref Expression
caovdig
Distinct variable groups:   ,,,   ,,,   ,,,   ,,,   ,,,   ,,,   ,,,   ,,,   ,,,

Proof of Theorem caovdig
StepHypRef Expression
1 caovdig.1 . . 3
21ralrimivvva 2791 . 2
3 oveq1 6080 . . . 4
4 oveq1 6080 . . . . 5
5 oveq1 6080 . . . . 5
64, 5oveq12d 6091 . . . 4
73, 6eqeq12d 2449 . . 3
8 oveq1 6080 . . . . 5
98oveq2d 6089 . . . 4
10 oveq2 6081 . . . . 5
1110oveq1d 6088 . . . 4
129, 11eqeq12d 2449 . . 3
13 oveq2 6081 . . . . 5
1413oveq2d 6089 . . . 4
15 oveq2 6081 . . . . 5
1615oveq2d 6089 . . . 4
1714, 16eqeq12d 2449 . . 3
187, 12, 17rspc3v 3053 . 2
192, 18mpan9 456 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359   w3a 936   wceq 1652   wcel 1725  wral 2697  (class class class)co 6073 This theorem is referenced by:  caovdid  6254  caovdi  6258  rngi  15668 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-uni 4008  df-br 4205  df-iota 5410  df-fv 5454  df-ov 6076
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